Bibliography for Milne-Simpson's Method

unabridged

 

  1. Parallel block PC methods with RKN-type correctors and Adams-type predictors.    
    Cong, Nguyen Huu; Minh, Nguyen Thi Hong    
    Int. J. Comput. Math. 74 (2000), no. 4, 509--527.
  2. Remarks on extended Milne's device for the Adams PC methods.  
    Fujii, Masatomo; Hayashi, Yuichi
    Bull. Fukuoka Univ. Ed. III  46  (1997), 23--30, MathSciNet.  
  3. Approximation of Ill-Posed Volterra Problems via Predictor-Corrector Regularization Methods  
    Patricia K. Lamm
    SIAM Journal on Applied Mathematics, Vol. 56, No. 2. (Apr., 1996), pp. 524-541, Jstor.  
  4. Analysis of Milne's device for the finite correction mode of the Adams PC methods. II.  
    Fujii, Masatomo
    Bull. Fukuoka Univ. Ed. III  45  (1996), 17--26, MathSciNet.  
  5. Unconditionally stable predictor-corrector methods for second order ordinary differential equations.   
    Garey, L. E.; Gladwin, C. J.   
    J. Differ. Equations Appl. 2 (1996), no. 4, 343--351, MathSciNet.   
  6. Analysis of Milne's device for the finite correction mode of the Adams PC methods. I.
    Fujii, Masatomo
    Bull. Fukuoka Univ. Ed. III 44 (1995), 21--34, MathSciNet.  
  7. Analysis of Milne's device for the finite correction mode of the Adams PC methods. II.
    Fujii, Masatomo
    Theory and applications of numerical calculation in science and technology (Japanese) (Kyoto, 1995).  Surikaisekikenkyusho Kokyuroku  No. 944 (1996), 21--29, MathSciNet.  
  8. On weak implicit and predictor-corrector methods.
    Platen, E.
    Mathematics and computers in simulation, 1995, vol. 38, no. 1/3, pp. 69, Ingenta.  
  9. Analysis of the Milne device for the finite correction mode of the Adams PC methods. I.
    Fujii, Masatomo
    Numerical analysis of ordinary differential equations and its applications (Kyoto, 1994), 75--89, World Sci. Publishing, River Edge, NJ, 1995, MathSciNet.  
  10. Spline approximations for neutral delay differential equations.
    Bellen, A.; Micula, G.
    Rev. Anal. Numér. Théor. Approx. 23 (1994), no. 2, 117--125, MathSciNet.  
  11. On marginal instability of predictor-corrector methods for first order ordinary differential equations.
    Garey, L. E.; Gladwin, C. J.
    Utilitas Math. 46 (1994), 143--153, MathSciNet.  
  12. Direct numerical spline methods for first-order Fredholm integro-differential equations.  
    Micula, Gheorghe; Fairweather, Graeme
    Rev. Anal. Numér. Théor. Approx.  22  (1993),  no. 1, 59--66, MathSciNet.  
  13. An extension of Milne's device for the Adams predictor-corrector methods.
    Fujii, Masatomo  
    Japan J. Indust. Appl. Math. 8 (1991), no. 1, 1--18, MathSciNet.  
  14. Quasilinear Multistep Methods and Variable Step Predictor-Corrector Methods for Neutral Functional Differential Equations  
    Zdzislaw Jackiewicz  
    SIAM Journal on Numerical Analysis, Vol. 23, No. 2. (Apr., 1986), pp. 423-452, Jstor.   
  15. Variable Step Size Predictor-Corrector Schemes for Second Kind Volterra Integral Equations  
    H. M. Jones, S. McKee  
    Mathematics of Computation, Vol. 44, No. 170. (Apr., 1985), pp. 391-404, Jstor.   
  16. One-Step Collocation: Uniform Superconvergence, Predictor-Corrector Method, Local Error Estimate  
    Marino Zennaro  
    SIAM Journal on Numerical Analysis, Vol. 22, No. 6. (Dec., 1985), pp. 1135-1152, Jstor.   
  17. The Convergence of Variable-Stepsize, Variable-Formula, Multistep Methods  
    M. Crouzeix, F. J. Lisbona  
    SIAM Journal on Numerical Analysis, Vol. 21, No. 3. (Jun., 1984), pp. 512-534, Jstor.   
  18. Numerical integration of retarded differential equations with periodic solutions.
    Arndt, H.; van der Houwen, P. J.; Sommeijer, B. P.
    Delay equations, approximation and application (Mannheim, 1984), 41--51, Internat. Schriftenreihe Numer. Math., 74, Birkhäuser, Basel, 1985, MathSciNet.  
  19. Families of methods for ordinary differential equations based on trigonometric polynomials.
    Neta, B.; Ford, C. H.
    J. Comput. Appl. Math. 10 (1984), no. 1, 33--38, MathSciNet.  
  20. Linear multistep methods with an increased range of absolute stability. (Chinese)
    Bao, Xue Song; Xu, Hong Yi; Wang, Chang Fu; Ze, Chan Fang
    Numer. Math. J. Chinese Univ. 6 (1984), no. 4, 311--318, MathSciNet.  
  21. Interpolation and error estimation in Adams PC-codes.    
    Stetter, Hans J.    
    SIAM J. Numer. Anal. 16 (1979), no. 2, 311--323.
  22. Parametric multistep methods. With Russian and German summaries.
    März, R.
    Seminarberichte [Seminar Reports], 18. Humboldt Universität, Sektion Mathematik, Berlin, 1979. iv+104 pp., MathSciNet.  
  23. Cubic spline functions and initial value problems.
    Patrício, Fernanda
    BIT 18 (1978), no. 3, 342--347, MathSciNet.  
  24. The Application of Linear Multistep Methods to Singular Initial Value Problems  
    Frank R. de Hoog, Richard Weiss  
    Mathematics of Computation, Vol. 31, No. 139. (Jul., 1977), pp. 676-690, Jstor.  
  25. A modification of Milne's method for the integration of ordinary differential equations. (Russian)  
    Glazkova, A. V.; Korobeinikov, V. V.
    Differential equations (Russian),  pp. 52--57, 111. Udmurt. Gos. Univ., Izhevsk, 1976, MathSciNet.  
  26. On Comparing Adams and Natural Spline Multistep Formulas  
    David R. Hill  
    Mathematics of Computation, Vol. 29, No. 131. (Jul., 1975), pp. 741-745, Jstor.  
  27. Some New Multistep Methods for Solving Ordinary Differential Equations  
    G. K. Gupta, C. S. Wallace  
    Mathematics of Computation, Vol. 29, No. 130. (Apr., 1975), pp. 489-500, Jstor.  
  28. The stability of modified predictor-corrector methods.
    Iyengar, Settaluri R. K.; Jain, M. K.
    J. Mathematical and Physical Sci. 8 (1974), 319--325, MathSciNet.  
  29. Sur les formules asymptotiques multiples de l'erreur en méthode aux différences finies.
    Ta Van Dbarnh
    Acta Sci. Vietnam. 9/10 (1974), 41--52, MathSciNet.  
  30. Stability and Convergence of Variable Order Multistep Methods  
    C. W. Gear, D. S. Watanabe  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 5. (Oct., 1974), pp. 1044-1058, Jstor.  
  31. The Effect of Variable Mesh Size on the Stability of Multistep Methods  
    C. W. Gear, K. W. Tu  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 5. (Oct., 1974), pp. 1025-1043, Jstor.  
  32. Exponential Fitting of Matricial Multistep Methods for Ordinary Differential Equations  
    E. F. Sarkany, W. Liniger  
    Mathematics of Computation, Vol. 28, No. 128. (Oct., 1974), pp. 1035-1052, Jstor.  
  33. Über zulässige Schrittweiten bei den Adams-Verfahren.
    Weissinger, J.
    Z. Angew. Math. Mech. 53 (1973), no. 2, 121--126, MathSciNet.  
  34. A Predictor-Corrector Method for a Certain Class of Stiff Differential Equations  
    Karl G. Guderley, Chen-Chi Hsu  
    Mathematics of Computation, Vol. 26, No. 117. (Jan., 1972), pp. 51-69, Jstor.   
  35. Predictor-Corrector Algorithms with Identical Regions of Stability  
    J. D. Lambert  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 2. (Jun., 1971), pp. 337-344, Jstor.   
  36. Cyclic Composite Multistep Predictor-Corrector Methods  
    John Donelson III, Eldon Hansen  
    SIAM Journal on Numerical Analysis, Vol. 8, No. 1. (Mar., 1971), pp. 137-157, Jstor.   
  37. On the Definite Integration of Singular Integrands  
    L. Fox; Linda Hayes  
    SIAM Review, Vol. 12, No. 3. (Jul., 1970), pp. 449-457, Jstor.  
  38. Numerical solution of an unharmonic oscillator eigenvalue problem by Milne's method.  
    Ezawa, Hiroshi; Nakamura, Koichi; Yamamoto, Yoshitaka
    Proc. Japan Acad.  46  1970 168--172, MathSciNet.  
  39. A Note on the Stability of Predictor-Corrector Techniques  
    James Case  
    Mathematics of Computation, Vol. 23, No. 108. (Oct., 1969), pp. 741-749, Jstor.   
  40. Numerical Stability of a One-Evaluation Predictor-Corrector Algorithm for Numerical Solution of Ordinary Differential Equations  
    R. W. Klopfenstein, R. S. Millman  
    Mathematics of Computation, Vol. 22, No. 103. (Jul., 1968), pp. 557-564, Jstor.   
  41. Spline Function Approximations for Solutions of Ordinary Differential Equations  
    Frank R. Loscalzo; Thomas D. Talbot  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 3. (Sep., 1967), pp. 433-445, Jstor.  
  42. An Analysis of the Numerical Stability of Predictor-Corrector Solutions of Nonlinear Ordinary Differential Equations  
    Robert J. Lambert  
    SIAM Journal on Numerical Analysis, Vol. 4, No. 4. (Dec., 1967), pp. 597-606, Jstor.   
  43. A lower estimate of the cumulative truncation error in Milne's method.
    Smith, A. C.
    Comput. J. 8 1965/1966 395--397, MathSciNet.  
  44. A generalization of the quadrature formulae of Simpson, Newton and Milne. (Russian)
    Ionesku, D. V.
    Soobsc. Akad. Nauk Gruzin. SSR 34 1964 11--18, MathSciNet.  
  45. Corrector Formulas for Multi-Step Integration Methods  
    T. E. Hull, A. C. R. Newbery  
    Journal of the Society for Industrial and Applied Mathematics, Vol. 10, No. 2. (Jun., 1962), pp. 351-369, Jstor.  
  46. An extension of Milne's three-point method.   
    Keitel, Glenn H.   
    J. Assoc. Comput. Mach. 3 (1956), 212--222, MathSciNet.  
  47. Estimation de l'erreur commise dans la méthode de M. W. E. Milne pour l'intégration d'un système de n équations différentielles du premier ordre. (French)
    Richter, Willy
    Thèse, Université de Neuchâtel, 1952. 43 pp., MathSciNet.  
  48. Sur l'erreur commise dans la méthode d'intégration de Milne. (French)
    Richter, Willy
    C. R. Acad. Sci. Paris 233, (1951). 1342--1344, MathSciNet.  
  49. Starting values for Milne-method integration of ordinary differential equations of first order, or of second order when first derivatives are absent.
    Marchant Methods.
    The method of Taylor's series MM-261. year unknown, 4 pp., MathSciNet.  
  50. Starting values for Milne-method integration of ordinary differential equations of the first order.
    Marchant Methods.
    The method of Milne. MM-260. year unknown, 11 pp., MathSciNet.  
  51. Milne method of step-by-step double integration of second order differential equations in which first derivatives are absent.
    Marchant Methods.
    MM-216A. year unknown, 6 pp., MathSciNet.  
  52. Milne method of step-by-step integration of ordinary differential equations when starting values are known.
    Marchant Methods.
    MM-216. year unknown, 10 pp., MathSciNet.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004